On the combinatorics of the toric Hilbert scheme

Diane Maclagan

University of California, Berkeley

October 27,
refreshments at 3:45pm


The toric Hilbert scheme parameterizes all ideals in a polynomial ring with the same multigraded Hilbert series as a given toric ideal. Such ideals were first introduced in a special case by Arnold, and in generality by Sturmfels. The ideals and scheme have also been studied by Korkina, Peeva and Gasharov, and Peeva and Stillman. One central open problem on toric Hilbert schemes is whether they are always connected. I will describe joint work with Rekha Thomas (Texas A&M) which connects this question to the Baues problem of geometric combinatorics. We construct a graph on the monomial ideals in scheme which is connected if and only if the scheme is connected.

Speaker's Contact Info: maclagan(at-sign)math.berkeley.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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